A Survey on Quantum Channel Capacities (1801.02019v1)

Abstract: Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. Here we review the properties of the quantum communication channel, the various capacity measures and the fundamental differences between the classical and quantum channels.

• The paper presents a comprehensive survey of quantum channel capacity definitions, including classical, quantum, private, and entanglement-assisted paradigms.
• It details methodologies and numerical insights for various channel models, highlighting challenges like decoherence and noise.
• The survey underscores future directions in error correction and experimental techniques to enhance the efficiency of quantum communication.

Overview of "A Survey on Quantum Channel Capacities"

The paper, "A Survey on Quantum Channel Capacities," serves as an extensive examination of the various theoretical frameworks and definitions associated with quantum channel capacities. It explores the potential and limitations of quantum information transmission, highlighting the differences and similarities with classical channels.

Quantum Communication Channels

Quantum channels extend classical communication channels by enabling the transmission of classical information, quantum information, and entanglement-assisted and private classical information. Unlike classical channels, quantum channels can transmit superpositions and entangled quantum states, providing a broader range of possibilities but also introducing new challenges related to quantum decoherence and noise.

Capacity Definitions

Several quantum channel capacity definitions are presented, each serving distinct operational paradigms:

1. Classical Capacity (C(𝒩)): Builds on classical mutual information and represents the capacity for transmitting classical information over a quantum channel using non-entangled states. It focuses on the maximum achievable data rate for reliable classical communication.
2. Quantum Capacity (Q(𝒩)): Reflects the ability to transmit quantum information, such as qubits, reliably over a noisy quantum channel. The capacity hinges on quantum error-correction protocols and is measured using coherent information.
3. Private Classical Capacity (P(𝒩)): This capacity denotes the secure transmission rate of classical information by ensuring that eavesdroppers gain negligible accessible information.
4. Entanglement-Assisted Classical Capacity (C_E(𝒩)): Utilizes pre-shared entanglement between sender and receiver, which can boost the classical capacity within noisy channels.
5. Zero-Error Capacity: This capacity measures the capability of a quantum channel to transmit information without errors, reflecting the fundamental limit of data transmission through noiseless channels.

Numerical Insights and Challenges

The paper provides several numerical insights into different channel models, such as Pauli, depolarizing, and amplitude damping channels. It examines the varying influences of noise and the ability to preserve quantum coherence, emphasizing the fundamental limits posed by quantum mechanics and the environment.

Implications and Future Directions

The research indicates that quantum channels could revolutionize computer science and telecommunications by providing fundamentally new solutions. However, this potential is accompanied by the stark realities of noise and limited capacity due to quantum decoherence. The paper suggests further exploration into improving these capacities through technological advancements in error correction and coherent communication protocols.

Conclusion

The paper concludes by underscoring the dual nature of quantum channels—they provide exciting new capabilities for secure, high-capacity information transmission but also present significant challenges. Ongoing theoretical and experimental work is essential to harness their full potential, necessitating an interdisciplinary approach combining physics, computer science, and engineering. Future breakthroughs in quantum communication could broaden the scope of quantum networks and computing, further integrating quantum mechanics with classical systems.